Mathematics > Differential Geometry

Abstract: We show that a properly immersed minimal hypersurface in M x R_+ equals some
M x {c} when M is a complete, recurrent n-dimensional Riemannian manifold with
bounded curvature. If on the other hand, M has nonnegative Ricci curvature with
curvature bounded below, the same result holds for any positive entire minimal
graph over M.